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Decomposition matrices for spin characters of symmetric groups. (English) Zbl 0651.20007
Let $$\tilde S_ n$$ be a double cover of the symmetric group $$S_ n$$. The faithful irreducible characters of $$\tilde S_ n$$ are called spin characters. In this paper a study of the p-decomposition numbers of such characters is initiated for odd prime integers p. A general technique is developed by a non-trivial modification of a corresponding technique for the characters of $$S_ n$$. Then the decomposition numbers are determined explicitly for $$p=3$$ and $$3\leq n\leq 11$$ with an ambiguity for $$n=9$$. The second author will deal separately with the cases $$p=5,7,11$$.
Reviewer: J.B.Olsson

##### MSC:
 20C30 Representations of finite symmetric groups 20C20 Modular representations and characters 20C25 Projective representations and multipliers
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##### References:
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